Diversity calculation
Masatoshi Katabuchi
2021/11/9
Course materials for 2021-11-9 AFEC at XTBG.
1 Objectives
- prepare species \(\times\) site matrix and trait data from csv files.
- calculate diversity indices.
2 Prerequisites
Did you install picante and FD?
install.packages("picante")
install.packages("FD")It’s better if you have those packages too.
install.packages("tidyverse")
install.packages("rmarkdown")
install.packages("DT")Load packages.
library(picante)
library(FD)
library(tidyverse)
library(rmarkdown)3 Data
3.1 Community
d <- read_csv("data/samp.csv")
d## # A tibble: 40 × 3
## Site Species abund
## <chr> <chr> <dbl>
## 1 Site1 Illicium_macranthum 1
## 2 Site1 Manglietia_insignis 0
## 3 Site1 Michelia_floribunda 0
## 4 Site1 Beilschmiedia_robusta 0
## 5 Site1 Neolitsea_chuii 0
## 6 Site1 Lindera_thomsonii 0
## 7 Site1 Actinodaphne_forrestii 0
## 8 Site1 Machilus_yunnanensis 0
## 9 Site2 Illicium_macranthum 1
## 10 Site2 Manglietia_insignis 2
## # … with 30 more rowsDT::datatable(d)First, we want to make a species \(\times\) site matrix. tapply is an useful function here.
tapply(d$abund, d$Species, sum)## Actinodaphne_forrestii Beilschmiedia_robusta Illicium_macranthum
## 4 2 5
## Lindera_thomsonii Machilus_yunnanensis Manglietia_insignis
## 5 2 3
## Michelia_floribunda Neolitsea_chuii
## 2 1samp <- tapply(d$abund, list(d$Site, d$Species), sum)
samp## Actinodaphne_forrestii Beilschmiedia_robusta Illicium_macranthum
## Site1 0 0 1
## Site2 0 2 1
## Site3 2 0 1
## Site4 2 0 1
## Site5 0 0 1
## Lindera_thomsonii Machilus_yunnanensis Manglietia_insignis
## Site1 0 0 0
## Site2 0 0 2
## Site3 2 2 0
## Site4 2 0 1
## Site5 1 0 0
## Michelia_floribunda Neolitsea_chuii
## Site1 0 0
## Site2 2 0
## Site3 0 0
## Site4 0 0
## Site5 0 1class(samp)## [1] "matrix" "array"3.2 Phylogeny
phylo <- read.tree("./data/dummy_tree.newick")
plot(phylo)
3.3 Traits
| Abbreviation | Trait | Unit |
|---|---|---|
| LMA | Leaf mass per area | g m-2 |
| LL | Leaf lifespans (longevity) | months |
| Amass | Maximum photosynthetic rates per unit mass | nnoml g-1 s-1 |
| Rmass | Dark resperation rates per unit mass | nnoml g-1 s-1 |
| Nmass | Leaf nitrogen per unit mass | % |
| Pmass | Leaf phosphorus per unit mass | % |
| WD | Wood density | g cm-3 |
| SM | Seed dry mass | mg |
trait <- read_csv("./data/dummy_trait.csv")
# trait <- read.csv("./data/dummy_trait.csv") is fine too.
DT::datatable(trait)3.4 Check how traits look like first
trait_long <- trait |>
pivot_longer(LMA:SM, names_to = "trait")
trait_long## # A tibble: 616 × 3
## sp trait value
## <chr> <chr> <dbl>
## 1 Acer_campbellii LMA 39.8
## 2 Acer_campbellii LL 7.08
## 3 Acer_campbellii Amass 985.
## 4 Acer_campbellii Rmass 54.7
## 5 Acer_campbellii Nmass 6.56
## 6 Acer_campbellii Pmass 0.42
## 7 Acer_campbellii WD 0.46
## 8 Acer_campbellii SM 0.39
## 9 Actinodaphne_forrestii LMA 69.2
## 10 Actinodaphne_forrestii LL 12.5
## # … with 606 more rowsggplot(trait_long, aes(x = value)) +
geom_histogram(position = "identity") +
facet_wrap(~ trait, scale = "free")
Probably we can do log-transformation for all the traits except for WD.
trait2 <- trait |>
mutate(logLMA = log(LMA),
logLL = log(LL),
logAmass = log(Amass),
logRmass = log(Rmass),
logNmass = log(Nmass),
logPmass = log(Pmass),
logSM = log(SM)) |>
dplyr::select(sp, logLMA, logLL, logAmass, logRmass, logNmass, logPmass, WD, logSM)
DT::datatable(trait2)trait2 |>
pivot_longer(logLMA:logSM, names_to = "trait") |>
ggplot(aes(x = value)) +
geom_histogram(position = "identity") +
facet_wrap(~ trait, scale = "free")
4 First-order metrics (without phylogeny or traits)
4.1 Species richness
samp > 0## Actinodaphne_forrestii Beilschmiedia_robusta Illicium_macranthum
## Site1 FALSE FALSE TRUE
## Site2 FALSE TRUE TRUE
## Site3 TRUE FALSE TRUE
## Site4 TRUE FALSE TRUE
## Site5 FALSE FALSE TRUE
## Lindera_thomsonii Machilus_yunnanensis Manglietia_insignis
## Site1 FALSE FALSE FALSE
## Site2 FALSE FALSE TRUE
## Site3 TRUE TRUE FALSE
## Site4 TRUE FALSE TRUE
## Site5 TRUE FALSE FALSE
## Michelia_floribunda Neolitsea_chuii
## Site1 FALSE FALSE
## Site2 TRUE FALSE
## Site3 FALSE FALSE
## Site4 FALSE FALSE
## Site5 FALSE TRUEapply(samp > 0, 1, sum)## Site1 Site2 Site3 Site4 Site5
## 1 4 4 4 34.2 Shannon
\(H' = - \sum_i^n p_i\mathrm{log}p_i\), where \(p_i\) is the relative abundance for species i.
shannon <- function(abund) {
p0 <- abund / sum(abund)
p <- p0[p0 > 0]
-sum(p * log(p))
}apply(samp, 1, shannon)## Site1 Site2 Site3 Site4 Site5
## 0.000000 1.351784 1.351784 1.329661 1.098612You don’t have to reinvent the wheel.
vegan::diversity(samp, index = "shannon")## Site1 Site2 Site3 Site4 Site5
## 0.000000 1.351784 1.351784 1.329661 1.0986124.3 Nonmetric Multidimensional Scaling (NMDS)
res_mds <- metaMDS(samp)## Run 0 stress 0
## Run 1 stress 9.984827e-05
## ... Procrustes: rmse 0.1288629 max resid 0.1986347
## Run 2 stress 9.088012e-05
## ... Procrustes: rmse 0.146334 max resid 0.2661121
## Run 3 stress 0
## ... Procrustes: rmse 0.1362746 max resid 0.2450818
## Run 4 stress 0.2297529
## Run 5 stress 9.690516e-05
## ... Procrustes: rmse 0.1288453 max resid 0.1986077
## Run 6 stress 0
## ... Procrustes: rmse 0.06293626 max resid 0.1021682
## Run 7 stress 0.1302441
## Run 8 stress 0.2297529
## Run 9 stress 0.09681034
## Run 10 stress 2.598084e-05
## ... Procrustes: rmse 0.1288389 max resid 0.1984968
## Run 11 stress 0
## ... Procrustes: rmse 0.04992979 max resid 0.08425844
## Run 12 stress 0
## ... Procrustes: rmse 0.09894182 max resid 0.1576147
## Run 13 stress 0
## ... Procrustes: rmse 0.04141783 max resid 0.05305252
## Run 14 stress 0
## ... Procrustes: rmse 0.09718763 max resid 0.1620504
## Run 15 stress 8.376017e-05
## ... Procrustes: rmse 0.12887 max resid 0.1986335
## Run 16 stress 0
## ... Procrustes: rmse 0.07972658 max resid 0.1274955
## Run 17 stress 0
## ... Procrustes: rmse 0.09541749 max resid 0.1724876
## Run 18 stress 0
## ... Procrustes: rmse 0.1004094 max resid 0.1380339
## Run 19 stress 8.005819e-05
## ... Procrustes: rmse 0.1288813 max resid 0.1986264
## Run 20 stress 0.1302441
## *** No convergence -- monoMDS stopping criteria:
## 15: stress < smin
## 1: stress ratio > sratmax
## 4: scale factor of the gradient < sfgrminplot(res_mds)
We can use the function ordiplot and orditorp to add text to the plot in place of points to make some more sense.
ordiplot(res_mds, type = "n")
orditorp(res_mds, display = "species", col = "red", air = 0.01)
orditorp(res_mds, display = "sites", cex = 1.25, air = 0.01)
5 Phylogenetic metrics
5.1 Branch length based metric
5.1.1 PD
res_pd <- pd(samp, phylo)
res_pd## PD SR
## Site1 1.000000 1
## Site2 3.022727 4
## Site3 2.909091 4
## Site4 3.136364 4
## Site5 2.454545 3You can always see the help.
?pd5.2 Distance based metric
cophenetic() creates distance matrices based on phylogenetic trees. Let’s see the first 5 species.
cophenetic(phylo)[1:5, 1:5]## Acer_campbellii Melia_toosendan Skimmia_arborescens
## Acer_campbellii 0.0000000 0.18181818 0.18181818
## Melia_toosendan 0.1818182 0.00000000 0.09090909
## Skimmia_arborescens 0.1818182 0.09090909 0.00000000
## Rhus_sylvestris 0.3636364 0.36363636 0.36363636
## Sterculia_nobilis 0.5454545 0.54545455 0.54545455
## Rhus_sylvestris Sterculia_nobilis
## Acer_campbellii 0.3636364 0.5454545
## Melia_toosendan 0.3636364 0.5454545
## Skimmia_arborescens 0.3636364 0.5454545
## Rhus_sylvestris 0.0000000 0.5454545
## Sterculia_nobilis 0.5454545 0.00000005.2.1 MPD
\(MPD = \frac{1}{n} \Sigma^n_i \Sigma^n_j \delta_{i,j} \; i \neq j\), where \(\delta_{i, j}\) is the pairwised distance between species i and j
res_mpd <- mpd(samp, cophenetic(phylo))
res_mpd## [1] NA 1.568182 1.454545 1.606061 1.636364The above vector shows MPD for each site.
5.2.2 MNTD
\(MNTD = \frac{1}{n} \Sigma^n_i min \delta_{i,j} \; i \neq j\), where \(min \delta_{i, j}\) is the minimum distance between species i and all other species in the community.
res_mntd <- mntd(samp, cophenetic(phylo))
res_mntd## [1] NA 1.181818 1.181818 1.295455 1.2727276 Functional metrics
6.1 Community weighted means (CWM)
\[ CWM_i = \frac{\sum_{j=1}^n a_{ij} \times t_{j}}{\sum_{j=1}^n a_{ij}} \]
tmp <- trait2 |>
filter(sp %in% colnames(samp))
tmp## # A tibble: 8 × 9
## sp logLMA logLL logAmass logRmass logNmass logPmass WD logSM
## <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 Actinodaphne_f… 4.24 2.53 5.01 2.17 0.412 -1.83 0.48 0.300
## 2 Beilschmiedia_… 3.61 3.09 5.72 3.53 1.75 -1.35 0.47 0.770
## 3 Illicium_macra… 5.66 4.75 3.27 0.793 -0.288 -3.51 0.4 -0.0305
## 4 Lindera_thomso… 4.47 3.70 5.49 3.02 0.626 -3.00 0.53 -0.734
## 5 Machilus_yunna… 4.26 3.36 4.65 2.69 0.239 -0.821 0.59 0.0770
## 6 Manglietia_ins… 6.22 5.24 3.10 0.255 -0.431 -3.91 0.45 -0.0513
## 7 Michelia_flori… 4.93 3.99 3.65 2.00 0.457 -3.91 0.54 0.621
## 8 Neolitsea_chuii 4.65 4.18 5.20 2.30 0.489 -2.12 0.43 -1.71(ab <- apply(samp, 1, sum))## Site1 Site2 Site3 Site4 Site5
## 1 7 7 6 3# inner product
(CWS <- samp %*% as.matrix(tmp[,-1]))## logLMA logLL logAmass logRmass logNmass logPmass WD
## Site1 5.664348 4.746496 3.274878 0.7929925 -0.2876821 -3.506558 0.40
## Site2 35.183333 29.374355 28.224437 12.3477060 3.2744092 -21.848797 3.32
## Site3 31.591321 23.923913 33.559838 16.5518827 2.2664479 -14.805146 3.60
## Site4 29.288871 22.431075 27.363748 11.4308299 1.3576312 -17.075208 2.87
## Site5 14.782600 12.622489 13.960935 6.1065359 0.8268364 -8.622554 1.36
## logSM
## Site1 -0.03045921
## Site2 2.64832362
## Site3 -0.74426629
## Site4 -0.94948167
## Site5 -2.47922681(CWM <- CWS / ab)## logLMA logLL logAmass logRmass logNmass logPmass WD
## Site1 5.664348 4.746496 3.274878 0.7929925 -0.2876821 -3.506558 0.4000000
## Site2 5.026190 4.196336 4.032062 1.7639580 0.4677727 -3.121257 0.4742857
## Site3 4.513046 3.417702 4.794263 2.3645547 0.3237783 -2.115021 0.5142857
## Site4 4.881479 3.738513 4.560625 1.9051383 0.2262719 -2.845868 0.4783333
## Site5 4.927533 4.207496 4.653645 2.0355120 0.2756121 -2.874185 0.4533333
## logSM
## Site1 -0.03045921
## Site2 0.37833195
## Site3 -0.10632376
## Site4 -0.15824694
## Site5 -0.826408946.2 Distance based metrics
6.2.1 Prepare a trait distance matrix
We have a data.fame of traits. First we need to prepare a trait matrix, then a distance matrix based on trait values.
trait_mat0 <- as.matrix(trait2[, -1])
rownames(trait_mat0) <- trait2$spLet’s see a subset of the trait matrix
trait_mat0[1:5, 1:5]## logLMA logLL logAmass logRmass logNmass
## Acer_campbellii 3.684118 1.957274 6.892692 4.002047 1.8809906
## Actinodaphne_forrestii 4.236712 2.527327 5.006359 2.173615 0.4121097
## Alnus_nepalensis 4.743366 4.010419 4.341335 2.022871 0.5007753
## Anneslea_fragrans 4.190715 3.293241 5.162211 3.703522 1.4632554
## Beilschmiedia_robusta 3.614964 3.085573 5.722441 3.526655 1.7544037Then, we will make trait distance matrix based on the Euclidean distance. There are other distance measures, for example Gower’s Distance, but we focus on the Euclidean distance today.
Before calulating distance, we need to make sure unit change in ditances have same for different traits. We will scale trait values so that then have mean = 0 and SD = 1. (e.g., \((X_i - \mu) / \sigma\))
trait_mat <- scale(trait_mat0)
par(mfrow = c(2, 2))
hist(trait_mat0[, "logLMA"])
hist(trait_mat[, "logLMA"])
hist(trait_mat0[, "WD"])
hist(trait_mat[, "WD"])
par(mfrow = c(1, 1))Now we can make a trait distance matrix.
trait_dm <- as.matrix(dist(trait_mat))Let’s see the first 5 species.
trait_dm[1:5, 1:5]## Acer_campbellii Actinodaphne_forrestii Alnus_nepalensis
## Acer_campbellii 0.000000 3.799360 5.216902
## Actinodaphne_forrestii 3.799360 0.000000 2.415031
## Alnus_nepalensis 5.216902 2.415031 0.000000
## Anneslea_fragrans 3.175911 2.335392 3.225141
## Beilschmiedia_robusta 2.545269 2.565063 3.638183
## Anneslea_fragrans Beilschmiedia_robusta
## Acer_campbellii 3.175911 2.545269
## Actinodaphne_forrestii 2.335392 2.565063
## Alnus_nepalensis 3.225141 3.638183
## Anneslea_fragrans 0.000000 1.579930
## Beilschmiedia_robusta 1.579930 0.0000006.2.2 MPD
mpd(samp, trait_dm)## [1] NA 4.288349 3.530805 3.961248 3.438008ses.mpd(samp, trait_dm)## ntaxa mpd.obs mpd.rand.mean mpd.rand.sd mpd.obs.rank mpd.obs.z
## Site1 1 NA NaN NA NA NA
## Site2 4 4.288349 3.677324 0.7776358 789 0.7857475
## Site3 4 3.530805 3.750847 0.8183244 434 -0.2688930
## Site4 4 3.961248 3.728399 0.8221437 641 0.2832223
## Site5 3 3.438008 3.752470 1.0277288 423 -0.3059774
## mpd.obs.p runs
## Site1 NA 999
## Site2 0.789 999
## Site3 0.434 999
## Site4 0.641 999
## Site5 0.423 9996.2.3 MNTD
mntd(samp, trait_dm)## [1] NA 2.504352 2.697074 1.873825 2.6135856.3 Branch length based metric
6.3.1 FD
We will make a functional dendrogram using clustering methods. We use UPGMA in this example.
t_clust <- hclust(dist(trait_mat), method = "average")
plot(t_clust)
6.3.2 More functional diversity metrics
res_fd <- dbFD(trait_mat[colnames(samp), ], samp)## FEVe: Could not be calculated for communities with <3 functionally singular species.
## FDis: Equals 0 in communities with only one functionally singular species.
## FRic: To respect s > t, FRic could not be calculated for communities with <3 functionally singular species.
## FRic: Dimensionality reduction was required. The last 5 PCoA axes (out of 7 in total) were removed.
## FRic: Quality of the reduced-space representation = 0.811349
## FDiv: Could not be calculated for communities with <3 functionally singular species.res_fd## $nbsp
## Site1 Site2 Site3 Site4 Site5
## 1 4 4 4 3
##
## $sing.sp
## Site1 Site2 Site3 Site4 Site5
## 1 4 4 4 3
##
## $FRic
## Site1 Site2 Site3 Site4 Site5
## NA 5.453089 2.917904 3.000656 3.553247
##
## $qual.FRic
## [1] 0.811349
##
## $FEve
## Site1 Site2 Site3 Site4 Site5
## NA 0.7595456 0.6769400 0.7085376 0.7584941
##
## $FDiv
## Site1 Site2 Site3 Site4 Site5
## NA 0.7301943 0.7617251 0.9166699 0.8261683
##
## $FDis
## Site1 Site2 Site3 Site4 Site5
## 0.000000 2.710994 1.842262 2.311159 2.042416
##
## $RaoQ
## Site1 Site2 Site3 Site4 Site5
## 0.000000 8.376023 4.005094 5.664467 4.379844
##
## $CWM
## logLMA logLL logAmass logRmass logNmass logPmass
## Site1 1.4467783 1.17548950 -1.38976382 -1.9975087 -0.88119735 -1.2775781
## Site2 0.5666449 0.55085046 -0.56218769 -0.8908026 -0.09004842 -0.8660119
## Site3 -0.1410729 -0.33319385 0.27087040 -0.2062427 -0.24084641 0.2088166
## Site4 0.3670613 0.03104745 0.01551229 -0.7298853 -0.34295985 -0.5718506
## Site5 0.4305791 0.56352114 0.11718014 -0.5812855 -0.29128834 -0.6020974
## WD logSM
## Site1 -1.0150179 -0.2191496
## Site2 -0.2744691 0.1665816
## Site3 0.1242879 -0.2907346
## Site4 -0.2341187 -0.3397288
## Site5 -0.4833418 -0.97019978 Computing Environment
devtools::session_info()## ─ Session info ───────────────────────────────────────────────────────────────
## setting value
## version R version 4.1.2 (2021-11-01)
## os macOS Big Sur 11.6
## system aarch64, darwin20.6.0
## ui unknown
## language (EN)
## collate en_US.UTF-8
## ctype en_US.UTF-8
## tz Asia/Shanghai
## date 2021-11-09
##
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## nlme * 3.1-152 2021-02-04 [1] CRAN (R 4.1.0)
## permute * 0.9-5 2019-03-12 [1] CRAN (R 4.1.0)
## picante * 1.8.2 2020-06-10 [1] CRAN (R 4.1.0)
## pillar 1.6.4 2021-10-18 [1] CRAN (R 4.1.1)
## pkgbuild 1.2.0 2020-12-15 [1] CRAN (R 4.1.0)
## pkgconfig 2.0.3 2019-09-22 [1] CRAN (R 4.1.0)
## pkgload 1.2.1 2021-04-06 [1] CRAN (R 4.1.0)
## prettyunits 1.1.1 2020-01-24 [1] CRAN (R 4.1.0)
## processx 3.5.2 2021-04-30 [1] CRAN (R 4.1.0)
## ps 1.6.0 2021-02-28 [1] CRAN (R 4.1.0)
## purrr * 0.3.4 2020-04-17 [1] CRAN (R 4.1.0)
## R6 2.5.0 2020-10-28 [1] CRAN (R 4.1.0)
## Rcpp 1.0.6 2021-01-15 [1] CRAN (R 4.1.0)
## readr * 2.0.2 2021-09-27 [1] CRAN (R 4.1.1)
## readxl 1.3.1 2019-03-13 [1] CRAN (R 4.1.0)
## remotes 2.4.0 2021-06-02 [1] CRAN (R 4.1.0)
## reprex 2.0.0 2021-04-02 [1] CRAN (R 4.1.0)
## rlang 0.4.11 2021-04-30 [1] CRAN (R 4.1.0)
## rmarkdown * 2.9 2021-06-15 [1] CRAN (R 4.1.0)
## rprojroot 2.0.2 2020-11-15 [1] CRAN (R 4.1.0)
## rstudioapi 0.13 2020-11-12 [1] CRAN (R 4.1.0)
## rvest 1.0.0 2021-03-09 [1] CRAN (R 4.1.0)
## sass 0.4.0 2021-05-12 [1] CRAN (R 4.1.0)
## scales 1.1.1 2020-05-11 [1] CRAN (R 4.1.0)
## sessioninfo 1.1.1 2018-11-05 [1] CRAN (R 4.1.0)
## stringi 1.6.2 2021-05-17 [1] CRAN (R 4.1.0)
## stringr * 1.4.0 2019-02-10 [1] CRAN (R 4.1.0)
## testthat 3.0.3 2021-06-16 [1] CRAN (R 4.1.0)
## tibble * 3.1.5 2021-09-30 [1] CRAN (R 4.1.1)
## tidyr * 1.1.4 2021-09-27 [1] CRAN (R 4.1.1)
## tidyselect 1.1.1 2021-04-30 [1] CRAN (R 4.1.0)
## tidyverse * 1.3.1 2021-04-15 [1] CRAN (R 4.1.1)
## tzdb 0.1.2 2021-07-20 [1] CRAN (R 4.1.1)
## usethis 2.0.1 2021-02-10 [1] CRAN (R 4.1.0)
## utf8 1.2.1 2021-03-12 [1] CRAN (R 4.1.0)
## vctrs 0.3.8 2021-04-29 [1] CRAN (R 4.1.0)
## vegan * 2.5-7 2020-11-28 [1] CRAN (R 4.1.0)
## vroom 1.5.4 2021-08-05 [1] CRAN (R 4.1.1)
## withr 2.4.2 2021-04-18 [1] CRAN (R 4.1.0)
## xfun 0.24 2021-06-15 [1] CRAN (R 4.1.0)
## xml2 1.3.2 2020-04-23 [1] CRAN (R 4.1.0)
## yaml 2.2.1 2020-02-01 [1] CRAN (R 4.1.0)
##
## [1] /opt/homebrew/lib/R/4.1/site-library
## [2] /opt/homebrew/Cellar/r/4.1.2/lib/R/library